The distribution of Voronoi cells generated by Southern California earthquake epicenters

Abstract

Fractional factorial designs are widely used in practice and typically chosen according to the minimum aberration criterion. A sequential algorithm is developed for constructing efficient fractional factorial designs. A construction procedure is proposed that only allows a design to be constructed from its minimum aberration projection in the sequential build-up process.To efficiently identify nonisomorphic designs, designs are divided into different categories according to their moment projection patterns. A fast isomorphism check procedure is developed by matching the factors using their delete-one-factor projections. A method is proposed for constructing minimum aberration designs using only a partial catalog of some good designs.

Statistical properties of Poisson-Voronoi tessellation cells in bounded regions

“…We have only considered the homogeneous Poisson point process, and further work may investigate how our results would change for other point patterns. For example, Schoenberg [3] studied the Voronoi tessellation of the locations of earthquakes in Southern California and found that the Pareto distribution to fit the cell area and perimeter well.…”

“…Ripley [2] discusses the importance of space subdivision methods to investigate spatial splines, and gives examples of different spatial point patterns for both simulated and real data to relate the subject to the estimation of distributions of the locations within a region using the Voronoi tessellation. The Voronoi tessellation has been applied in different sciences such as in seismology where Schoenberg [3] investigated the distribution of cell areas in a Voronoi tessellation based on the locations of earthquakes in Southern California; astronomy [4][5][6] to discover how galaxies are distributed in space; to investigate the conditions of the habitat of animals when they are establishing territories [7]; in agriculture for maximal weed suppression in plant crops [8] and to study atomic crystals [9], liquids [10], glasses [11], and wireless networks [12,13]. An application of constrained Voronoi tessellation is used in micro-structure modeling [14] where a new space subdivision method is introduced using inverse Monte Carlo based on conditions such as moving the randomly placed points until their geometric features obey a particular distribution.…”

Distribution of Cell Area in Bounded Poisson Voronoi Tessellations with Application to Secure Local Connectivity

“…In that case, φ 1 = φ 2 = 0, and the void of the point P always contains the corner of the quadrant in its interior. The size of the void is still given by equation (3).…”

“…When the distribution of the seeds follows the stationary Poisson Point Process (PPP) with a finite intensity λ > 0, the random tessellation is widely-known as the Poisson Voronoi Tessellation (PVT) [1], [2]. Since the concept of PVT is quite fundamental, it accepts a wide range of applications from geo-sciences and astronomy, e.g., [3], [4] to telecommunications [5].…”

Could Geometry Demystify Patterns of Earth Quakes and Aftershocks? An Answer is Yes

“…Abe and Suzuki (2007) used the correlation to relate seismicity with aftershocks. Schoenberg et al (2008) provide the geometric view of the distribution of Voronoi cells generated stress. Métivier et al (2009) announced the evidence of earthquake as triggered by the solid earth tides.…”